Question

The points $A(a,b+c),B(b,c+a)$ and $C(c,a+b)$ are:

• A. collinear
• B. doesn't lie in the same plane
• C. doesn't lie on the same line
• D. nothing can be said

Answer 1

The correct option is A collinear

Slope of $AB=\frac{(c+a)-(b+c)}{b-a}=\frac{a-b}{b-a}=-1$
Slope of $BC=\frac{(b+a)-(a+c)}{c-b}=\frac{b-c}{c-b}=-1$
This is only possible if three points lie on same line.
Therefore collinear.